The address 0.0.0.0 may only be used as the address of an outgoing packet when a computer is learning which IP address it should use. It is never used as a destination address. Addresses starting with "0." are sometimes used for broadcasts to directly connected devices.

If you see addresses starting with a "0." in logs they are probably in use on your network, which might be as small as a computer connected to a home gateway.

This block was assigned by the IETF, the organization that develops Internet protocols, in the Standard document, RFC 1122, and is further documented in the Best Current Practice document RFC 6890. IANA is listed as the registrant to make it clear that this network is not assigned to any single organization.

These documents can be found at:
http://datatracker.ietf.org/doc/rfc1122
http://datatracker.ietf.org/doc/rfc6890